YAhwT: economics homework help!

[iamme]

i'm stuck on one problem and call upon the great wisdom of atot

Suppose that a semiconductor plant's production function is q = 5LK, where q is its output rate, L is the amount of labor it uses per period of time, and K is the amount of capital it uses per period of time. Suppose that the price of labor is $1 a unit and the price of capital is $2 per unit.

a). The firm's VP wants you to figure out what combination of inputs the plant should use for 20 units of output.
b). 40 units of output?
c). compare a). and b). and explain the scale effect
d). Same as a)., but the price of labor has risen to $2 per unit.

now, i know that the slope is marginal product of labor (MPL) over marginal product of capital (MPK) = 1/2.

i can't seem to figure out how to draw the isocost curve and find the optimal inputs.

any help is appreciated

 

[iamme]

lil bump for managerial economics fun!

 

[puffff]

go to office hours.

 

[theNEOone]

wow, i should DEFINITELY know this, but it's been a while so i'm gonna cut myself some slack. i can definitely find the answer for you once i get home and can dig through my notes from school (if i still have them).


=|

 

[TuxDave]

Originally posted by: puffff
go to office hours.

hahaha

 

[TuxDave]

Originally posted by: theNEOone
wow, i should DEFINITELY know this, but it's been a while so i'm gonna cut myself some slack. i can definitely find the answer for you once i get home and can dig through my notes from school (if i still have them).


=|

Heh.. I'm not anywhere close to a business major but answering A,B and D looks really simple. I have no idea what the scale effect is so I can't answer C

 

[iamme]

well, i'm a bit confused as to which are the isocost and which is the isoquant lines. also, i believe they are supposed to be tangent at a certain point, which would indicate optimal input ratios.

off to the library i go to figure it out

 

[UncleWai]

I will try to chime in since I am preping for my tutor session for intermediate econ at the moment.

your total cost function is:
tc = 1L + 2K
MU of L = 5K
MU of K = 5L

MU L / MU K = K/L = 2

so you know K= 2L

plug this in to q = 5LK
you get Q = 5L *(2L)
Q = 20units

you should know how to do this by now?

Hope I am right :beer:

 

[iamme]

Originally posted by: UncleWai
I will try to chime in since I am preping for my tutor session for intermediate econ at the moment.

your total cost function is:
tc = 1L + 2K
MU of L = 5K
MU of K = 5L

MU L / MU K = K/L = 2

so you know K= 2L

plug this in to q = 5LK
you get Q = 5L *(2L)
Q = 20units

you should know how to do this by now?

Hope I am right :beer:

that's how i got my answer, but, i got this from my text:

K/L = (price of labor)/(price of capital)
i ended up with L = 2K

same method, but it seems that the answers would get flip flopped. am i looking at something wrong?

 

[TuxDave]

The way I ended up doing was....

Quantity = 5*L*K
Cost = L + 2*K

L = Quantity/(5*K)
L = Cost - 2*K

Optimality in this problem is when these slopes are equal right?

dL/dK = -Quantity/(5K^2)
dL/dK = -2

Solve?

So for part a) I get Quantity = 20 therefore K = sqrt(2) and L = 2*sqrt(2)